Megabits per second to Gibibytes per day conversion

How to convert megabits per second to gibibytes per day?

Certainly! Let's walk through the conversion of 1 Megabit per second (Mbps) to Gibibytes per day, considering both base 10 (decimal) and base 2 (binary) systems.

Base 10 (Decimal) System

1 Megabit (Mb) is equivalent to $10^6$ bits.

1. Convert Megabits to bits:

$1 \text{ Mbps} = 1 \times 10^6 \, \text{bits per second}$

2. Convert bits per second to bits per day:

$\text{bits per day} = 1 \times 10^6 \, \text{bits per second} \times 60 \, \text{seconds per minute} \times 60 \, \text{minutes per hour} \times 24 \, \text{hours per day}$

$\text{bits per day} = 1 \times 10^6 \times 60 \times 60 \times 24$

$\text{bits per day} = 86,400,000,000 \, \text{bits per day}$

3. Convert bits to bytes:

$1 \text{ byte} = 8 \text{ bits}$

$\text{bytes per day} = \frac{86,400,000,000 \, \text{bits per day}}{8}$

$\text{bytes per day} = 10,800,000,000 \, \text{bytes per day}$

4. Convert bytes to Gigabytes (GB):

$1 \text{ Gigabyte (GB)} = 10^9 \, \text{bytes}$

$\text{GB per day} = \frac{10,800,000,000 \, \text{bytes per day}}{10^9}$

$\text{GB per day} = 10.8 \, \text{GB per day}$

5. Convert GB to Gibibytes (GiB):

$1 \text{ GiB} = 2^{30} \, \text{bytes} \approx 1.073 \times 10^9 \, \text{bytes}$

$\text{GiB per day} = \frac{10,800,000,000 \, \text{bytes per day}}{1.073 \times 10^9}$

$\text{GiB per day} \approx 10.06 \, \text{GiB per day}$

Base 2 (Binary) System

Using binary conventions where 1 Megabit = $2^{20}$ bits:

1. Convert Megabits to bits:

$1 \text{ Mbps} = 2^{20} \, \text{bits per second} \approx 1,048,576 \, \text{bits per second}$

2. Convert bits per second to bits per day:

$\text{bits per day} = 1,048,576 \, \text{bits per second} \times 60 \times 60 \times 24$

$\text{bits per day} \approx 90,509,447,680 \, \text{bits per day}$

3. Convert bits to bytes:

$1 \text{ byte} = 8 \text{ bits}$

$\text{bytes per day} = \frac{90,509,447,680 \, \text{bits per day}}{8}$

$\text{bytes per day} \approx 11,313,680,960 \, \text{bytes per day}$

4. Convert bytes to Gibibytes (GiB):

$1 \text{ GiB} = 2^{30} \, \text{bytes} = 1,073,741,824 \, \text{bytes}$

$\text{GiB per day} = \frac{11,313,680,960 \, \text{bytes per day}}{1,073,741,824}$

$\text{GiB per day} \approx 10.54 \, \text{GiB per day}$

Real-World Examples for Other Quantities of Megabits per Second

1. 10 Mbps Internet Connection:

   • Decimal System:

     $10.8 \, \text{GB per day} \times 10 = 108 \, \text{GB per day}$

     $10.06 \, \text{GiB per day} \times 10 = 100.6 \, \text{GiB per day}$

   • Binary System:

     $10.54 \, \text{GiB per day} \times 10 = 105.4 \, \text{GiB per day}$

2. 50 Mbps Internet Connection:

   • Decimal System:

     $10.8 \, \text{GB per day} \times 50 = 540 \, \text{GB per day}$

     $10.06 \, \text{GiB per day} \times 50 = 503 \, \text{GiB per day}$

   • Binary System:

     $10.54 \, \text{GiB per day} \times 50 = 527 \, \text{GiB per day}$

3. 100 Mbps Internet Connection:

   • Decimal System:

     $10.8 \, \text{GB per day} \times 100 = 1080 \, \text{GB per day}$

     $10.06 \, \text{GiB per day} \times 100 = 1006 \, \text{GiB per day}$

   • Binary System:

     $10.54 \, \text{GiB per day} \times 100 = 1054 \, \text{GiB per day}$

These examples help illustrate how the conversion scales with higher bandwidth rates and how the results differ slightly between decimal and binary systems.